A farmer is interested in whether there is any variation in the weights of apple

Question

A farmer is interested in whether there is any variation in the weights of apples between two trees. Data collected from the two trees are as follows: Tree1: pi_1 = 201, x_1 = 8.2 0z, s_1 = 0.6 0z Tree 2: pi_2 = 251 x_2 = 7.8 0z, s_2 = 0.5 0z Her null hypothesis and alternative hypothesis are: H_0: sigma^2_1 =sigma^2_2, and H_sigma: sigma^2_1 > sigma^2_2 (a) Determine the teat statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. (a) Determine the P-value for this test. Show all work; writing the correct P value, without supporting work. will receive no credit. (c) Is there sufficient evidence to justify the rejection of H_1 at the sigpilicanee level of 0.05? Explain.

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   sigma1^2 / sigma2^2   <=   1  
Ha:    sigma1^2 / sigma2^2   >   1  
              
As we can see, this is a    right   tailed test.  
Getting the test statistic, as              
s1 =    0.6          
s2 =    0.5          
              
Thus, F = s1^2/s2^2 =    1.44   [ANSWER]

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b)  
              
As

df1 = n1 - 1 =    200         
df2 = n2 - 1 =    250          

Then, as this is right tailed,

P = 0.003159811 [ANSWER]

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c)

As P < 0.05, then yes, there is significant evidence to justify the rejection of Ho at 0.05 level.   

              

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